Lightly grease a 9-inch round cake pan, 10-inch oven-safe skillet, or similar baking dish. Arrange the 12 frozen rolls inside with a little space between each one.

Cover the pan loosely and let the rolls thaw and rise according to the package directions, usually for 3–5 hours depending on the product and room temperature. They should look noticeably puffy and nearly doubled before you add the cheese.

Melt the butter and stir in the finely minced garlic, Italian seasoning, chopped parsley, and optional kosher salt. Mix until the herbs are distributed evenly throughout the butter.

When the rolls have completed their main rise, carefully separate or partially cut between them without slicing all the way through. Brush the garlic herb butter over the tops and into the spaces between the rolls.

Tuck small portions of shredded mozzarella into the spaces between the rolls. Scatter the remaining mozzarella over the top, then finish with the finely grated Parmesan.

Let the assembled rolls rest for 20–30 minutes while the oven heats to 350°F (175°C). This short rest gives the dough time to relax and puff slightly before baking.

Bake at 350°F (175°C) for 20–25 minutes, until the rolls are golden brown and the cheese is fully melted. If the cheese browns before the centers are baked, loosely tent the pan with foil.

Brush the baked rolls with any remaining garlic butter and sprinkle with extra chopped parsley. Serve warm, pulling the rolls apart at the table while the cheese is still soft and stretchy.